39 research outputs found
New Bounds for the Harmonic Energy and Harmonic Estrada index of Graphs
Let be a finite simple undirected graph with vertices and edges. The Harmonic energy of a graph , denoted by , is defined as the sum of the absolute
values of all Harmonic eigenvalues of . The Harmonic Estrada index of a graph , denoted by , is defined as
where are the - of .
In this paper we present some new bounds for and in terms of number of vertices, number of edges and the sum-connectivity index
On the variable inverse sum deg index
Several important topological indices studied in mathematical chemistry are expressed in the following way Puv∈E(G) F(du, dv), where F is a two variable function that satisfies the condition F(x, y) = F(y, x), uv denotes an edge of the graph G and du is the degree of the vertex u. Among them, the variable inverse sum deg index ISDa, with F(du, dv) = 1/(dua + dva), was found to have several applications. In this paper, we solve some problems posed by Vukičević [1], and we characterize graphs with maximum and minimum values of the ISDa index, for a < 0, in the following sets of graphs with n vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbon
Some new aspects of main eigenvalues of graphs
An eigenvalue of the adjacency matrix of a graph is said to be main if the all-1 vector is non-orthogonal to the associated eigenspace. This paper explores some new aspects of the study of main eigenvalues of graphs, investigating specifically cones over strongly regular graphs and graphs for which the least eigenvalue is non-main. In this case, we characterize paths and trees with diameter-3 satisfying the property. We may note that the importance of
least eigenvalues of graphs for the equilibria of social and economic networks was recently uncovered in literature.publishe